FINAL-STATE INTERACTIONS IN 3 MESON SYSTEMS - ANALYSIS OF DATA ON (P)OVER-BAR-P-]PI-0-PI-0-PI-0 AND ETA-ETA-PI-0 AT REST

We provide a theoretical and computational formalism for the study of three-body annihilation of ppBAR. It includes (i) an analysis of three-body equations with the purpose of extracting the leading singularities and (ii) an analysis of low-energy pipi, KKBAR, 7171, and pieta amplitudes and the reconstruction of them from available experimental data. Based on this formalism, we perform an analysis of data on ppBAR --> pi0pi0pi0 and etaetapi0 at rest. The data are fitted well by pure S-1(0) annihilation and require two I = 0,J(PC) = 0++ resonances with M1 = 1335 +/- 40 mev, GAMMA1 = 255(+60\-40) MeV, and M2 = 1505 +/- 20 MeV, GAMMA2 = 150 +/- 20 MeV. The latter explains features of the data previously interpreted in an alternative way as due to A(x)(1515) with J(PC) = 2++. As a second step, we evaluate the magnitude of the amplitudes due to triangle singularities which result from rescatterings of outgoing mesons. Taking into account these rescattering processes enhances the magnitudes of low-lying resonances, notably f0(975).